AN ANALOGUE OF CIRCULAR UNITS FOR PRODUCTS OF ELLIPTIC CURVES

We construct certain elements in the motivic cohomology group $H^3_{\mathcal{M}}(E\times E',\mathbb{Q}(2))$, where $E$ and $E'$ are elliptic curves over $\mathbb{Q}$. When $E$ is not isogenous to $E'$ these elements are analogous to circular units in real quadratic fields, as they com...

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Bibliographic Details
Published inProceedings of the Edinburgh Mathematical Society Vol. 47; no. 1; pp. 35 - 51
Main Authors Baba, Srinath, Sreekantan, Ramesh
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.02.2004
Subjects
Beilinson conjectures
class number
motivic cohomology
Beilinson conjectures
motivic cohomology
class number
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ISSN0013-0915
1464-3839
DOI10.1017/S001309150200113X

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Summary:We construct certain elements in the motivic cohomology group $H^3_{\mathcal{M}}(E\times E',\mathbb{Q}(2))$, where $E$ and $E'$ are elliptic curves over $\mathbb{Q}$. When $E$ is not isogenous to $E'$ these elements are analogous to circular units in real quadratic fields, as they come from modular parametrizations of the elliptic curves. We then find an analogue of the class-number formula for real quadratic fields, which specializes to the usual quadratic class-number formula when $E$ and $E'$ are quadratic twists. AMS 2000 Mathematics subject classification: Primary 11F67; 14G35. Secondary 11F11; 11E45; 14G10
Bibliography:istex:8C8E113FDF71A477D7E664729078BEB72FDFEACF
ArticleID:00113
Present address: Max Planck Institute of Mathematics, Vivatsgasse 7, D-53111 Bonn, Germany.
PII:S001309150200113X
ark:/67375/6GQ-L8T2NF30-B
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0013-0915
1464-3839
DOI:10.1017/S001309150200113X